Senior district judge Emma Arbuthnot found his comments about running Miller over menacing and racially aggravating.

Miller said Philipps’ posts “genuinely shocked” her and made her feel “angry” “violated” and “upset” that “somebody on social media could post racist and personal words about me.”

Miller also hired security guards following the threat to run her over.

The judge also convicted 50-year-old Philipps for comments he made after reading an article about a migrant, Arthur Sube, who was reported to have turned down a five-bedroom council house for his family of eight children.

Following the publication of the article about Sube in September 2016, Philipps wrote: “Please will someone smoke this ghastly insult to our country? Why should I pay tax to feed these monkeys? A return to Planet of the Apes is not acceptable.”

Arbuthnot did not find this to be menacing and acquitted Phillips of the charge related to that post.

In a second post, he wrote: “I will open the bidding. £2,000 in cash for the first person to carve Arnold Sube into pieces, piece of shit.” Arbuthnot found this post to be menacing but not racially aggravated.

Philipps – who also holds the titles Lord Hungerford, Lord de Moleyns, and Lord Strange of Knockin – insisted he is not racist. He accepted that he had written the posts but said they were not publicly visible and were not menacing.

He told the court: “I know a number of Muslims who are dear friends. My own mother is an immigrant from the very same continent [as Miller].”

Philipps represented himself in court and admitted during his evidence that he was “incandescent” after Miller’s legal challenge.

“She’s left a third-world country to come to Britain,” he added. “It’s not for first generation immigrants to behave the way Gina Miller did.”

He insisted his posts were meant as “an opening for debate”, and continued: “It’s how I express myself, not for everyone’s taste or liking.

“If you’re in the public eye, people are going to say nasty things about you. It’s the rough and tumble of public life.”

Arbuthnot said: “I had no doubt that the first post was menacing ... You were offering money to have her killed.”

She said: “Looking at the language you use to Ms Miller ... ‘fucking jumper’. That is not political debate.”

The judge added: “To some who don’t know you they would perceive the offers of bounty as menacing.”

She said the posts would “cause apprehension in a reasonable person reading them in this multi-racial country we live in”.

Arbuthnot found the post about Miller to be racially aggravated and told Philipps he faces a prison sentence when he is sentenced on Thursday.

Kate Mulholland from the Crown Prosecution Service said: “This threat caused extreme concern to Gina Miller and although Lord St Davids claimed his Facebook friends would have been tolerant of his views, they were open to the public.

“No-one should have these kind of menacing comments made to them or about them and where there is evidence of an offence the CPS and police will bring a prosecution.”